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On algebraicity and rationality conditions of the sum of a power series. (Russian) Zbl 0622.32009

It is shown that a convergent series \(f(z)=\sum_{k\geq 0}\alpha_ kz^ k\) defines a rational function iff there is a rational function \(F(z_ 1,z_ 2)=\sum_{m,n\geq 0}a_{mn}z^ m_ 1z^ n_ 2\) such that \(\sum_{k}\alpha_ kz^ k=\sum_{k}a_{kk}z^ k\).
Reviewer: A.Pankov

MSC:

32B05 Analytic algebras and generalizations, preparation theorems
32A05 Power series, series of functions of several complex variables
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